Tootfinder

Robin Green Function Estimates and a Model of Mammalian Lungs
Guy David, Stefano Decio, Max Engelstein, Marcel Filoche, Svitlana Mayboroda, Marco Michetti
https://arxiv.org/abs/2507.13168

Robin Green Function Estimates and a Model of Mammalian Lungs
The present paper establishes delicate properties of the Green function with Robin boundary conditions, in particular, elucidating the nature of the passage between the Dirichlet-like and Neumann-like behavior. This yields sharp quantifiable bounds on the corresponding harmonic measure and proves the phase transition in the behavior of the total flow earlier conjectured in physics literature in concert with the efficacy of mammalian lungs.

Inference on Common Trends in a Cointegrated Nonlinear SVAR
James A. Duffy, Xiyu Jiao
https://arxiv.org/abs/2507.22869 https://arxiv.org/pdf/2507.22869

Inference on Common Trends in a Cointegrated Nonlinear SVAR
We consider the problem of performing inference on the number of common stochastic trends when data is generated by a cointegrated CKSVAR (a two-regime, piecewise-linear SVAR; Mavroeidis, 2021), using a modified version of the Breitung (2002) multivariate variance ratio test that is robust to the presence of nonlinear cointegration (of a known form). To derive the asymptotics of our test statistic, we prove a fundamental LLN-type result for a class of stable but nonstationary autoregressive pro…